Two long parallel conductors S1 and S2 are separated by a distance 10… | JEE Main 2022 (27 Jun, Shift 2)

Q62JEE Main 2022 · 27 JUN · SHIFT 2Difficult

Moving Charge in a Magnetic Field

Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).

A charged particle of 3 $\pi$ coulomb is passing through the point P with velocity $\vec{v} = (2\hat{i} + 3\hat{j})$ m/s; where $\hat{i}$ and $\hat{j}$ represents unit vector along x & y axis respectively.

The force acting on the charged particle is $4\pi \times 10^{-5}(-x\hat{i} + 2\hat{j})$ N. The value of x is:

Show answer and solution

Answer: (c)

$P$ is 4 cm below $S_1$ and 6 cm above $S_2$ ; both currents are along $+x$ .
From $S_1$ : $B_1 = \dfrac{\mu_0 (4)}{2\pi(0.04)} = 2 \times 10^{-5}\text{ T}$ along $-\hat{k}$ . From $S_2$ : $B_2 = \dfrac{\mu_0 (2)}{2\pi(0.06)} = \tfrac{2}{3} \times 10^{-5}\text{ T}$ along $+\hat{k}$ .
Net $\vec{B} = -\tfrac{4}{3} \times 10^{-5}\,\hat{k}\text{ T}$ .
$\vec{F} = q\vec{v} \times \vec{B} = 3\pi(2\hat{i} + 3\hat{j}) \times (-\tfrac{4}{3} \times 10^{-5}\hat{k}) = 4\pi \times 10^{-5}(-3\hat{i} + 2\hat{j})\text{ N}$
So $x = 3$ , answer (c).

Report a mistake

Moving Charge in a Magnetic Field question from JEE Main 2022 (27 Jun, Shift 2)

More questions on Moving Charge in a Magnetic Field